Literature Cited
M. A. Lavrent'ev, “Stability in the Liouville theorem,” Dokl. Akad. Nauk SSSR,95, 925–926 (1954).
M. A. Lavrent'ev, “Quasi-conformal mappings,” Tr. III Vsesoyuzn. Matem. S'ezda, Vol.3, Obzornye Doklady (1958), pp. 198–208.
Yu. G. Reshetnyak, “On stability of conformal mappings in multidimensional spaces,” Sibirsk. Matem. Zh.,8, No. 1, 111–134 (1967).
Yu. G. Reshetnyak, “Stability theorems for mappings of bounded distortion,” Sibirsk. Matem. Zh.,9, No. 3, 667–684 (1968).
Yu. G. Reshetnyak, “Bounds for certain differential operators with finite dimensional kernel,” Sibirsk. Matem. Zh.,11, No. 2 (1970).
N. N. Ural'tseva, “Bounds for a modulus of continuity of the first derivatives for a class of elliptic differential equations,” Tr. Matem. Seminara LOMI (1968).
S. L. Sobolev, On Some Applications of Functional Analysis to Mathematical Physics [in Russian], Vol. 1, Izd. LGU (1950).
A. I. Koshelev, “On boundedness in Lp of derivatives of solutions of elliptic differential equations,” Matem. Sb.,38, No. 3, 359–372 (1956).
B. A. Rozenfel'd, Non-Euclidean Geometry [in Russian], Izd. Akad. Nauk SSSR, Moscow (1955).
Yu. G. Reshetnyak, “On extremal properties of mappings with bounded distortion,” Sibirsk. Matem. Zh.,10, No. 6, 1300–1310 (1969).
S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press (1963).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 11, No. 5, pp. 1121–1139, September–October, 1970.
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Reshetnyak, Y.G. On stability bounds in the liouville theorem on conformal mappings of multidimensional spaces. Sib Math J 11, 833–846 (1970). https://doi.org/10.1007/BF00967843
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DOI: https://doi.org/10.1007/BF00967843